Figure shows a large closed cylindrical tank containing water. Initially, the air trapped above the water surface has a height `h_(0)` and pressure `2p_(0)` where `rh_(0)` is the atmospheric pressure. There is a hole in the wall of the tank at a depth `h_(1)` below the top from which water comes out. A long vertical tube is connected as shown.

Find the speed with which water comes out of the hole

Options

A. ` (1)/(rho ) [ p_0 - rho g (h_1- 2 h_0 )]^(1//2) `
B. `[ (2)/(rho ) [ p_0 + rho g (h_1 - h_0)]]^(1//2 ) `
C. `[ (3)/( rho ) [ p_0 + rho g ( h_1 + h_0)]]^(1//2) `
D. `[ (4)/(rho) [ p_0 + rho g (h_1 - h_2 )] ] ^(1//2) `

Answer

B

Explanation

Appling Bernoulli just inside and outside hole: `2P_(0)+rhog(h_(1)-h_(0))+0=P_(0)+(1)/(2)rhoV^(2)`